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Theorems · Definition · category theory

CategoryTheory.Limits.limit.lift

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        (F : CategoryTheory.Functor J C) →
          [inst_2 : CategoryTheory.Limits.HasLimit F] →
            (c : CategoryTheory.Limits.Cone F) → c.pt ⟶ CategoryTheory.Limits.limit F

The morphism from the cone point of any other cone to the limit object.

Defined in
Mathlib.CategoryTheory.Limits.HasLimits
Cited by
48 results in Mathlib
Foundations
Depth 7 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimit

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Limits.limit.lift_π · cited by 266limit.lift_πCategoryTheory.Limits.prod.lift · cited by 123prod.liftCategoryTheory.Limits.pullback.lift · cited by 114pullback.liftCategoryTheory.Limits.limit.lift_π_assoc · cited by 95limit.lift_π_assocCategoryTheory.Limits.terminal.from · cited by 77terminal.fromCategoryTheory.Limits.Pi.lift · cited by 53Pi.liftCategoryTheory.Limits.equalizer.lift · cited by 19equalizer.liftCategoryTheory.Limits.Multiequalizer.lift · cited by 18Multiequalizer.liftCategoryTheory.Functor.pointwiseRightKanExtension · cited by 13Functor.pointwiseRightKan…CategoryTheory.Limits.WidePullback.lift · cited by 12WidePullback.liftCategoryTheory.Limits.limit.pre · cited by 11limit.preCategoryTheory.Limits.limit.post · cited by 9limit.postCategoryTheory.Limits.colimitLimitToLimitColimit · cited by 6Limits.colimitLimitToLimi…CategoryTheory.Limits.limitCompCoyonedaIsoCone · cited by 3Limits.limitCompCoyonedaI…AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp · cited by 3GlueData.ιInvAppCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Limits.Cone.pt · cited by 1298Cone.ptCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Limits.limit · cited by 346Limits.limitCategoryTheory.Limits.HasLimit · cited by 226Limits.HasLimitCategoryTheory.Limits.IsLimit.lift · cited by 167IsLimit.liftCategoryTheory.Limits.limit.isLimit · cited by 146limit.isLimitlimit.liftCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by74

Results whose statement or proof uses this declaration.